estimate

Syntax

Description

EstMdl = estimate(Mdl,y)
estimates the unknown parameters of the conditional variance model object
Mdl with the observed univariate time series
y, using maximum likelihood. EstMdl is a
fully specified conditional variance model object that stores the results. It is the
same model type as Mdl (see garch, egarch, and gjr).

EstMdl = estimate(Mdl,y,Name,Value)
estimates the conditional variance model with additional options specified by one or
more Name,Value pair arguments. For example, you can specify to
display iterative optimization information or presample innovations.

estimate treats non-NaN elements in
Mdl as equality constraints, and does not estimate
the corresponding parameters.

y — Single path of response datanumeric column vector

Single path of response data, specified as a numeric column vector. The
software infers the conditional variances from y, i.e.,
the data to which the model is fit.

y is usually an innovation series with mean 0 and
conditional variance characterized by the model specified in
Mdl. In this case, y is a
continuation of the innovation series E0.

y can also represent an innovation series with mean 0
plus an offset. A nonzero Offset signals the inclusion of
an offset in Mdl.

The last observation of y is the latest
observation.

Data Types: double

Name-Value Pair Arguments

Specify optional
comma-separated pairs of Name,Value arguments. Name is
the argument name and Value is the corresponding value.
Name must appear inside quotes. You can specify several name and value
pair arguments in any order as
Name1,Value1,...,NameN,ValueN.

'E0' — Presample innovationsnumeric column vector

Presample innovations, specified as the comma-separated pair
consisting of 'E0' and a numeric column vector. The
presample innovations provide initial values for the innovations process
of the conditional variance model Mdl. The
presample innovations derive from a distribution with mean 0.

'Offset0' — Initial innovation mean model offset estimatescalar

By default, estimate sets the initial estimate to
the sample mean of y.

Data Types: double

'Options' — Optimization optionsoptimoptions optimization controller

Optimization options, specified as the comma-separated pair consisting of
'Options' and an optimoptions optimization
controller. For details on altering the default values of the optimizer, see optimoptions or fmincon in Optimization
Toolbox™.

For example, to change the constraint tolerance to 1e-6,
set Options = optimoptions(@fmincon,'ConstraintTolerance',1e-6,'Algorithm','sqp').
Then, pass Options into estimate using 'Options',Options.

By default, estimate uses the same default
options as fmincon, except Algorithm is 'sqp' and ConstraintTolerance is 1e-7.

The number of coefficients in Leverage0 must equal
the number of lags associated with nonzero coefficients in the leverage
polynomial (Leverage), as specified in
LeverageLags.

Data Types: double

Notes

NaNs in the presample or estimation data indicate
missing data, and estimate removes them. The
software merges the presample data (E0 and
V0) separately from the effective sample data
(y), and then uses list-wise deletion to remove
rows containing at least one NaN. Removing
NaNs in the data reduces the sample size, and can
also create irregular time series.

estimate assumes that you synchronize the
presample data such that the latest observations occur
simultaneously.

If you specify a value for Display, then it takes
precedence over the specifications of the optimization options
Diagnostics and Display.
Otherwise, estimate honors all selections related to
the display of optimization information in the optimization
options.

If you do not specify E0 and V0,
then estimate derives the necessary presample
observations from the unconditional, or long-run, variance of the
offset-adjusted response process.

For all conditional variance models, V0
is the sample average of the squared disturbances of the
offset-adjusted response data y.

For GARCH(P,Q) and
GJR(P,Q) models,
E0 is the square root of the average
squared value of the offset-adjusted response series
y.

Variance-covariance matrix of maximum likelihood estimates of model
parameters known to the optimizer, returned as a numeric matrix.

The rows and columns associated with any parameters estimated by maximum
likelihood contain the covariances of estimation error. The standard errors
of the parameter estimates are the square root of the entries along the main
diagonal.

The rows and columns associated with any parameters that are held fixed as
equality constraints contain 0s.